NEET Planet and Satellite MCQs & PYQs

Assertion (A) is true. The Moon maintains a stable orbit around Earth. Reason (R) is false. There is no radially outward force balancing Earth's gravity. Instead, Earth's gravitational force *is* the centripetal force required for the Moon's orbit. The Moon's tangential velocity prevents it from falling directly into Earth while gravity pulls it in.

Assertion (A) is false. Only an inverse-square force leads to stable, closed elliptical orbits. An inverse cube law would lead to unstable orbits. Reason (R) is also false. Kepler's third law, \( T^2 propto r^3 \), is a direct consequence of the inverse-square law. If the law changes, this relation no longer holds. Therefore, both (A) and (R) are false.

Assertion (A): For any central force, the orbit is always planar and contains the center of force (Earth's center). So (A) is true.

Reason (R): Gravitational force is a central force, so net torque is zero. This implies conservation of angular momentum, \(\vec{L} = \vec{r} \times \vec{p}\), which means the orbital plane is fixed. So (R) is true. (R) correctly explains (A).

Assertion (A): The Moon has sufficient tangential velocity to orbit the Earth, so it continuously 'falls around' the Earth instead of falling into it. So (A) is true.nReason (R): Calculations show that the gravitational force from the Sun on the Moon is indeed greater than that from the Earth on the Moon. So (R) is true.nHowever, the Sun's attraction does not prevent the Moon from falling to Earth; the Moon's orbital velocity does. Thus, (R) is not the correct explanation for (A).

Assertion (A) is true due to inertia (Newton's First Law). Reason (R) is true as orbital speed \(v = \sqrt{GM/r}\) decreases with increasing \(r\).

However, R does not explain A; A is a consequence of inertia, not the relation between orbital speed and radius.

Assertion (A) is true because weightlessness in orbit is due to continuous freefall. Reason (R) is false; gravitational force *is* present and provides the centripetal force for orbit.

Both Assertion (A) and Reason (R) are true. The gravitational force being a central force (R) ensures angular momentum conservation, which mandates that the orbital plane must contain the center of the earth (A).

Assertion (A) is false; moving a satellite to a higher orbit requires external work, increasing its total energy. Reason (R) is false in this context; \(\Delta K = -\Delta U\) applies only when mechanical energy is conserved, which is not the case when external work is done.

The comet tail always points away from the Sun due to solar wind and radiation pressure pushing on the sublimated material. Solar radiation does vaporize volatile materials, forming the tail, but this vaporization itself doesn't fully explain the direction. Hence, both statements are true, but R is not the correct explanation of A.

For the geostationary satellite, $T_1 = 24\text{ hours}$, $r_1 = R + 5R = 6R$. For the second satellite, $r_2 = R + 2R = 3R$. Using Kepler's third law $T^2 \propto r^3$, we have $T_2 = T_1 \left(\frac{r_2}{r_1}\right)^{3/2} = 24 \left(\frac{3R}{6R}\right)^{3/2} = 24 \left(\frac{1}{2}\right)^{3/2} = 6\sqrt{2}\text{ hours}$.